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Identification of Joint Distributions in Dependent Factor Models. Conditionally accepted at Econometric Theory.
This paper studies linear factor models that have arbitrarily dependent factors. Assuming that the coefficients are known and that their matrix representation satisfies rank conditions, we identify the nonparametric joint distribution of the unobserved factors using first and then second-order partial derivatives of the log characteristic function of the observed variables. In conjunction with these identification strategies the mean and variance of the vector of factors are identified. The main result provides necessary and sufficient conditions for identification of the joint distribution of the factors. In an illustrative example, we show identification of an earnings dynamics model with a subset of arbitrarily dependent income shocks. Closed-form formulas lead to estimators that converge uniformly and despite being based on inverse Fourier transforms have tight confidence bands around their theoretical counterparts in Monte Carlo simulations.
Identification of Additive and Polynomial Models of Mismeasured Regressors Without Instruments, with Xavier D’Haultfœuille and Arthur Lewbel. Conditionally accepted at Journal of Econometrics.
We show nonparametric point identification of a measurement error model with covariates that can be interpreted as invalid instruments. Our main contribution is to replace standard exclusion restrictions with the weaker assumption of additivity in the covariates. Measurement errors are ubiquitous and additive models are popular, so our results combining the two should have widespread potential application. We also identify a model that replaces the nonparametric function of the mismeasured regressor with a polynomial in that regressor and other covariates. This allows for rich interactions between the variables, at the expense of introducing a parametric restriction. Our identification proofs are constructive, and so can be used to form estimators. We establish root-n asymptotic normality for one of our estimators.
We identify and estimate coefficients in a linear factor model in which factors are allowed to be arbitrarily dependent. Given a statistical dependence structure on the unobservables, rank conditions on the matrix representation and restrictions on coefficients, the unknown coefficients are identified under nonnormality assumptions. The identification strategy transforms the system of equations into a functional equation using log characteristic functions. By ruling out polynomial functions which correspond to normal distributions, we show that the unknown coefficients uniquely solve the functional equation. Identification is illustrated in the classical errors-in-variables model with arbitrarily dependent unobserved regressors and in a panel data moving average process in which subsets of the shocks are allowed to be arbitrarily dependent. We propose an extremum estimator based on second-order partial derivatives of the empirical log characteristic function that is root-n consistent and asymptotically normal. In Monte Carlo simulations the estimator produces similar results to a GMM estimator based on higher-order moments, and is more robust to different amounts of measurement error and distributional choices of unobservables.